Method for precoding to mitigate nonlinear distortions and precoder for performing the same

ABSTRACT

A method for precoding to mitigate nonlinear distortions and a precoder for performing the same are disclosed. The precoder for mitigating distortions of a communication signal may include a filter configured to generate a filtering signal based on a third signal and filter coefficients corresponding to a selected signal generated based on a first signal, a second signal, and the third signal, and a modulo operator configured to generate the third signal by performing a modulo operation on the second signal, wherein the second signal is generated based on the first signal and the filtering signal.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims the benefit of Korean Patent Application No.10-2021-0034676 filed on Mar. 17, 2021, in the Korean IntellectualProperty Office, the entire disclosure of which is incorporated hereinby reference for all purposes.

BACKGROUND 1. Field of the Invention

One or more example embodiments relate to a precoding method formitigating nonlinear distortions and a precoder for performing the same.

2. Description of Related Art

Recently, it has become necessary to implement low cost, small sizeshort distance optical links used in massive constructions such as adata center, a metro network, an optical access network. In addition, asa modulation method, pulse amplitude modulation (PAM), one of the directdetection modulation methods, is being widely used. More particularly,PAM-4 has been adopted as a modulation method for IEEE 802.3bs, which isa 400 Gbps ethernet standard, in consideration of power consumption andimplementation complexity.

In case of a direct detection method, interference between symbols suchas inter-symbol interference (ISI) may occur due to a bandwidthlimitation of an electronic device. In addition, since the opticaldevices being used are low cost, nonlinear distortion may occur. Thedistortion is an amplitude-dependent skew according to a level or anamplitude of a signal and an amplitude-dependent noise.

Conventionally, a pre-equalizer such as a Tomlinson-Harashima Precoder(THP) is used in a transmitter to reduce ISI generated due to abandwidth limitation. This is a modified method of mitigating ISI by afeed-forward equalizer (FFE) in a receiver. In a conventional THPstructure, a modulo operator is added to a FFE filter used in thereceiver.

Since a conventional THP may remove post-cursor ISI based on a channelresponse characteristic of a channel, it may be used in a transmitter ofa system with a small bandwidth capability. A filter used in a THP maybe designed to have a linear characteristic and configured with samechannel response characteristic regardless of a level of a signal as afilter. Thus, it may be difficult to solve the problem of lineardistortions occurring at each level of the signal.

The above description has been possessed or acquired by the inventor(s)in the course of conceiving the present disclosure and is notnecessarily an art publicly known before the present application isfiled.

SUMMARY

Example embodiments provide a precoding method for mitigating nonlineardistortions of a signal as well as inter-symbol interference (ISI).

However, the technical aspects are not limited to the aforementionedaspects, and other technical aspects may be present.

According to an aspect, there is provided a precoder for mitigatingdistortions of a communication signal including a filter configured togenerate a filtering signal based on a third signal and filtercoefficients corresponding to a selected signal generated based on afirst signal, a second signal, and the third signal, and a modulooperator configured to generate the third signal by performing a modulooperation on the second signal, wherein the second signal may begenerated based on the first signal and the filtering signal.

The filter may include a level detector configured to generate theselected signal, a plurality of delay elements configured to outputdelayed signals by delaying the third signal, a plurality of selectorsconfigured to select and output the filter coefficients based on theselected signal, a plurality of multipliers configured to multiply thethird signal and the delayed signals by the filter coefficients, and anadder configured to output the filtering signal by adding multiplicationresults obtained by the plurality of multipliers.

The level detector may include an adder configured to generate a levelsignal based on the first to third signals and a comparator configuredto output the selected signal based on the level signal and a pluralityof comparison signals.

The plurality of delay elements may include a first delay elementconfigured to output a first delayed signal by delaying the third signaland a second delay element configured to output a second delayed signalby delaying the first delayed signal.

The plurality of selectors may include a first selector configured tooutput a first filter coefficient corresponding to the third signal, asecond selector configured to output a second filter coefficientcorresponding to the first delayed signal, and a third selectorconfigured to output a third filter coefficient corresponding to thesecond delayed signal.

According to an aspect, there is provided a precoder for mitigatingdistortions of a communication signal, including a filter configured togenerate a filtering signal based on a third signal and filtercoefficients respectively corresponding to a plurality of selectedsignals generated based on a first signal, a second signal, and thethird signal, and a modulo operator configured to generate the thirdsignal by performing a modulo operation on the second signal, whereinthe second signal is generated based on the first signal and thefiltering signal.

The filter may include a level detector configured to generate theplurality of selected signals, a plurality of delay elements configuredto output delayed signals by delaying the third signal, a plurality ofselectors configured to select and output the filter coefficients basedon the plurality of selected signals respectively, a plurality ofmultipliers configured to multiply the third signal and the delayedsignals by the filter coefficients, and an adder configured to outputthe filtering signal by adding multiplication results obtained by theplurality of multipliers.

The level detector may include an adder configured to generate a levelsignal based on the first to third signals, a plurality of delayelements configured to output delayed signals by delaying the levelsignal, and a plurality of comparators configured to output theplurality of selected signals based on the level signal and the delayedlevel signals respectively.

According to an aspect, there is provided a method for precoding tomitigate distortions of a communication signal, including generating afiltering signal based on a third signal and filter coefficientsselected based on a selected signal generated based on a first signal, asecond signal, and the third signal, and generating the third signal byperforming a modulo operation on the second signal, wherein the secondsignal is generated based on the first signal and the filtering signal.

The generating of the filtering signal may include generating theselected signal; outputting delayed signals by delaying the thirdsignal, selecting and outputting the filter coefficients based on theselected signal, multiplying the third signal and the delayed signals bythe filter coefficients, and outputting the filtering signal by addingmultiplication results.

The generating of the selected signal may include generating a levelsignal based on the first to third signals and outputting the selectedsignal based on the level signal and a plurality of comparison signals.

The outputting by delaying may include outputting a first delayed signalby delaying the third signal and outputting a second delayed signal bydelaying the first delayed signal.

The selecting and outputting of the filter coefficients may includeoutputting a first filter coefficient corresponding to the third signal,outputting a second filter coefficient corresponding to the firstdelayed signal, and outputting a third filter coefficient correspondingto the second delayed signal.

The outputting of the filtering signal may include generating aplurality of selected signals, outputting the delayed signals bydelaying the third signal, selecting and outputting the filtercoefficients based on the plurality of selected signals respectively,multiplying the third signal and the delayed signal by the filtercoefficients, and outputting the filtering signal by addingmultiplication results.

The generating of the plurality of selected signals may includegenerating a level signal based on the first to third signals,outputting delayed level signals by delaying the level signal, andoutputting the plurality of selected signals based on the level signaland the delayed level signals respectively.

Additional aspects of example embodiments will be set forth in part inthe description which follows and, in part, will be apparent from thedescription, or may be learned by practice of the disclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

These and/or other aspects, features, and advantages of the inventionwill become apparent and more readily appreciated from the followingdescription of example embodiments, taken in conjunction with theaccompanying drawings of which:

FIG. 1 illustrates a communication system according to an exampleembodiment;

FIG. 2 illustrates an example of the precoder of FIG. 1 ;

FIG. 3 illustrates the level detector of FIG. 2 ;

FIG. 4 illustrates another example of the precoder of FIG. 1 ;

FIG. 5 illustrates the level detector of FIG. 4 ; and

FIGS. 6A and 6B illustrates a level signal of a level detector and acomparison signal of a level detector respectively.

DETAILED DESCRIPTION

The following detailed structural or functional description is providedas an example only and various alterations and modifications may be madeto the examples. Here, the examples are not construed as limited to thedisclosure and should be understood to include all changes, equivalents,and replacements within the idea and the technical scope of thedisclosure.

Terms, such as first, second, and the like, may be used herein todescribe components. Each of these terminologies is not used to definean essence, order or sequence of a corresponding component but usedmerely to distinguish the corresponding component from othercomponent(s). For example, a first component may be referred to as asecond component, and similarly the second component may also bereferred to as the first component.

It should be noted that if it is described that one component is“connected”, “coupled”, or “joined” to another component, a thirdcomponent may be “connected”, “coupled”, and “joined” between the firstand second components, although the first component may be directlyconnected, coupled, or joined to the second component.

The singular forms “a”, “an”, and “the” are intended to include theplural forms as well, unless the context clearly indicates otherwise. Itwill be further understood that the terms “comprises/comprising” and/or“includes/including” when used herein, specify the presence of statedfeatures, integers, steps, operations, elements, and/or components, butdo not preclude the presence or addition of one or more other features,integers, steps, operations, elements, components and/or groups thereof.

Unless otherwise defined, all terms, including technical and scientificterms, used herein have the same meaning as commonly understood by oneof ordinary skill in the art to which this disclosure pertains. Terms,such as those defined in commonly used dictionaries, are to beinterpreted as having a meaning that is consistent with their meaning inthe context of the relevant art, and are not to be interpreted in anidealized or overly formal sense unless expressly so defined herein.

Hereinafter, example embodiments will be described in detail withreference to the accompanying drawings. When describing the exampleembodiments with reference to the accompanying drawings, like referencenumerals refer to like components and a repeated description relatedthereto will be omitted.

FIG. 1 illustrates a communication system according to an exampleembodiment.

A communication system 10 may include a precoder 100 to mitigate anonlinear distortion and inter-symbol interference (ISI) in a signalbeing transmitted and received. The precoder 100 may be implemented at atransmitter of the communication system 10. A demodulator may beimplemented at a receiver corresponding to the precoder 100. FIG. 1illustrates only a configuration to mitigate a nonlinear distortion andISI in the communication system 10. Thus, it shall be understood thatdescriptions of general components of the communication system 10 areomitted.

The precoder 100 may remove the ISI occurring in the communicationsystem 10 using an inverse function H(Z)−1 of a channel response H(Z)through a filter 200. The precoder 100 may limit a maximum swing valuetransmitted for stabilizing the filter 200 to remove post-cursor ISI byperforming a modulo operation Mod 2M by a modulo operator 130.

The precoder 100 may output a third signal Y_(n) by performing precodingwhen a first signal X_(n) is input. The filter 200 may generate afiltering signal Z_(n) based on the third signal Y_(n). A mixer 110 maygenerate a second signal X_(n)′ based on the first signal X_(n) and thefiltering signal Z_(n). The second signal X_(n)′ may be a signalremoving the filtering signal Z_(n) from the first signal X_(n). Themodulo operator 130 may generate the third signal Y_(n) by performing amodulo operation on the second signal X_(n)′. The third signal Y_(n) maybe a signal transmitted to the receiver.

The demodulator 150 may restore a received signal r_(n) received fromthe receiver. The received signal r_(n) may be a signal including noisewhen passing through a channel. A modulo operator 153 may restore thereceived signal r_(n) by performing the modulo operation Mod 2M on thereceived signal r_(n).

The precoder 100 may mitigate a nonlinear distortion occurring in thecommunication system 10 by selecting filter coefficients havingnonlinear characteristics based on a level of a signal. The filter 200may compensate for the nonlinear distortion by selecting the filtercoefficients to generate the filtering signal Z_(n) based on the firstsignal X_(n), the second signal X_(n)′ and the third signal Y_(n).

FIG. 2 illustrates an example of the precoder of FIG. 1 .

The precoder 100 may include the modulo operator 130 and the filter 200.The filter 200 may include a level detector 300, a plurality of delayelements 210-1 and 210-2, a plurality of selectors 230-1 to 230-3, aplurality of multipliers 250-1 to 250-3, and an adder 270.

The level detector 300 may generate a selected signal Sel based on thefirst signal X_(n), the second signal X_(n)′, and the third signalY_(n). The level detector 300 may generate a level signal L_(n) based onthe first signal X_(n), the second signal X_(n)′ and the third signalY_(n) and may output the selected signal Sel based on a level value ofthe level signal L_(n). For example, the selected signal Sel may have avalue of 1 to m (m is a natural number) according to a level value ofthe level signal L_(n).

The selectors 230-1 to 230-3 may output filter coefficients based on theselected signal Sel. For example, the selectors 230-1 to 230-3 mayoutput filter coefficients corresponding to the selected signal Selamong a plurality of filtering signals h₄₁ to h_(4m), h₃₁ to h_(3m), andh₂₁ to h_(2m). For example, when the selected signal Sel is k (k is anatural number greater than or equal to 1 and less than or equal to m),the selectors 230-1 to 230-3 may output the filter coefficients h_(4k),h_(3k), and h_(2k) respectively.

The delay elements 210-1 and 210-2 may output delayed signals bydelaying the third signal Y_(n). For example, the first delay element210-1 may output a first delayed signal Y_(n-1) by delaying the thirdsignal Y_(n) by a unit of time and the second delay element 210-2 mayoutput a second delayed signal Y_(n-2) by delaying the first delayedsignal Y_(n-1) by a unit of time. That is, the second delayed signalY_(n-2) may be an output signal of the third signal Y_(n) delayed by twounits of time.

The multipliers 250-1 to 250-3 may multiply the third signal Y_(n), thefirst delayed signal Y_(n-1) and the second delayed signal Y_(n-2) bythe filter coefficient and may output multiplication results. Forexample, the first multiplier 250-1 may multiply the second delayedsignal Y_(n-2) by the filter coefficient output from the first selector230-1 and may output a multiplication result, the second multiplier250-2 may multiply the first delayed signal Y_(n-1) by the filtercoefficient output from the second selector 230-2 and may output amultiplication result, and the third multiplier 250-3 may multiply thethird signal Y_(n) by the filter coefficient output from the thirdselector 230-3 and may output a multiplication result.

The adder 270 may add the multiplication results obtained by themultipliers 250-1 to 250-3 and output the filtering signal Z_(n). Forexample, the adder 270 may output the filtering signal Z_(n) by addingall multiplication results output from the first multiplier 250-1 to thethird multiplier 250-3 respectively. For example, when the selectedsignal Sel is k so that filter coefficients output from the selectors230-1 to 230-3 are the filter coefficient h_(4k), h_(3k), and h_(2k)respectively, the filtering signal Z_(n) may be expressed by Equation 1.Z _(n) =h _(2k) Y _(n) +h _(3k) Y _(n-1) +h _(4k) Y _(n-2)  [Equation 1]

FIG. 3 illustrates the level detector of FIG. 2 .

The level detector 300 may include an adder 310 to generate a levelsignal L_(n) based on a first signal X_(n), a second signal X_(n), and athird signal Y_(n) and a comparator 330 to output the selected signalSel based on the level signal L_(n) and a plurality of comparisonsignals L_(th1) to L_(thm).

The level signal L_(n) output from the adder 310 may be expressed byEquation 2.L _(n) =X _(n) −X _(n) ′+Y _(n)  [Equation 2]

The comparator 330 may determine which comparison signal among theplurality of comparison signals L_(th1) to L_(thm) has a same levelvalue as the level signal L_(n). For example, when a difference of levelvalues between the level signal L_(n) and a comparison signal Lt_(hk) isless than or equal to a threshold value, the comparator 330 maydetermine that the level signal L_(n) has a same level value as thecomparison signal L_(thk).

The comparator 330 may output the selected signal Sel corresponding tothe comparison signal Lt_(hk) which is determined to have a same levelvalue as the level signal L_(n). For example, the comparator 330 mayoutput k as the selected signal Sel corresponding to the comparisonsignal L_(thk) having a same level value as the level signal L_(n).

When the first signal X_(n) is a pulse amplitude modulation-4 (PAM-4)signal, the level signal L_(n) may include four signal levels as shownin FIG. 6A. The plurality of comparison signals Lt_(h1) to L_(thm) maycorrespond to six signal levels as shown in FIG. 6B, and in this case,the selected signal Sel may be output as any one of 1 to 6.

FIG. 4 illustrates another example of the precoder of FIG. 1 and FIG. 5illustrates the level detector of FIG. 4 .

The precoder 100 may include the filter 200 to generate the filteringsignal Z_(n) using three selected signals Sel1 to Sel3. Since theprecoder 100 of FIG. 4 may be same as the precoder 100 of FIG. 2 exceptfor the level detector 300, a duplicate description of the configurationto perform the same operation is omitted.

The level detector 300 may further include a plurality of delay elements350-1 and 350-2. The delay elements 350-1 and 350-2 may output delayedsignals by delaying the level signal L_(n) output from the adder 310.For example, the first delay element 350-1 may output a first delayedlevel signal L_(n-1) by delaying the level signal L_(n) by a unit oftime and the second delay element 350-2 may output a second level signalL_(n-2) by delaying the first delayed level signal L_(n-1) by a unit oftime. That is, the second delayed level signal L_(n-2) may be a delayedsignal of the level signal L_(n) by two units of time.

The level detector 300 may further include a plurality of comparators330-1 to 330-3. The respective comparators 330-1 to 330-3 may performthe same operation as the comparator 330 of FIG. 3 . For example, thecomparators 330-1 to 330-3 may output the first selected signal Sel1,the second selected signal Sel2, and the third selected signal Sel3respectively based on the level signal L_(n), the first delayed levelsignal L_(n-1), and the second delayed level signal L_(n-2).

The first selected signal Sel1, the second selected signal Sel2, and thethird selected signal Sel3 may be input to the corresponding selectors230-1 to 230-3. That is, since the selected signals Sel1 to Sel3different from each other may be input to each of the selectors 230-1 to230-3, the selectors 230-1 to 230-3 may output filter coefficientsdifferent from each other and the filtering signal Z_(n) may begenerated based on the different filter coefficients. For example, whenthe selected signals Sel1 to Sel3 are p, q, and r (p, q, and r arenatural numbers greater than or equal to 1 and less than or equal to m)respectively, the filtering signal Z_(n) may be expressed by Equation 3.Z _(n) =h _(2p) Y _(n) +h _(3q) Y _(n-1) +h _(4r) Y _(n-2)  [Equation 3]

The components described in the example embodiments may be implementedby hardware components including, for example, at least one digitalsignal processor (DSP), a processor, a controller, anapplication-specific integrated circuit (ASIC), a programmable logicelement, such as a field programmable gate array (FPGA), otherelectronic devices, or combinations thereof. At least some of thefunctions or the processes described in the example embodiments may beimplemented by software, and the software may be recorded on a recordingmedium. The components, the functions, and the processes described inthe example embodiments may be implemented by a combination of hardwareand software.

The examples described herein may be implemented using hardwarecomponents, software components and/or combinations thereof. Aprocessing device may be implemented using one or more general-purposeor special-purpose computers, such as, for example, a processor, acontroller and an arithmetic logic unit (ALU), a DSP, a microcomputer,an FPGA, a programmable logic unit (PLU), a microprocessor or any otherdevice capable of responding to and executing instructions in a definedmanner. The processing device may run an operating system (OS) and oneor more software applications that run on the OS. The processing devicealso may access, store, manipulate, process, and create data in responseto execution of the software. For purpose of simplicity, the descriptionof a processing device is used as singular; however, one skilled in theart will appreciate that a processing device may include multipleprocessing elements and multiple types of processing elements. Forexample, the processing device may include a plurality of processors, ora single processor and a single controller. In addition, differentprocessing configurations are possible, such as parallel processors.

The software may include a computer program, a piece of code, aninstruction, or some combination thereof, to independently or uniformlyinstruct or configure the processing device to operate as desired.Software and data may be embodied permanently or temporarily in any typeof machine, component, physical or pseudo equipment, computer storagemedium or device, or in a propagated signal wave capable of providinginstructions or data to or being interpreted by the processing device.The software also may be distributed over network-coupled computersystems so that the software is stored and executed in a distributedfashion. The software and data may be stored by one or morenon-transitory computer-readable recording mediums.

The methods according to the above-described example embodiments may berecorded in non-transitory computer-readable media including programinstructions to implement various operations of the above-describedexample embodiments. The media may also include, alone or in combinationwith the program instructions, data files, data structures, and thelike. The program instructions recorded on the media may be thosespecially designed and constructed for the purposes of exampleembodiments, or they may be of the kind well-known and available tothose having skill in the computer software arts. Examples ofnon-transitory computer-readable media include magnetic media such ashard disks, floppy disks, and magnetic tape; optical media such asCD-ROM discs, DVDs, and/or Blue-ray discs; magneto-optical media such asoptical discs; and hardware devices that are specially configured tostore and perform program instructions, such as read-only memory (ROM),random access memory (RAM), flash memory (e.g., USB flash drives, memorycards, memory sticks, etc.), and the like. Examples of programinstructions include both machine code, such as produced by a compiler,and files containing higher-level code that may be executed by thecomputer using an interpreter.

The above-described devices may be configured to act as one or moresoftware modules in order to perform the operations of theabove-described examples, or vice versa.

A number of example embodiments have been described above. Nevertheless,it should be understood that various modifications may be made to theseexample embodiments. For example, suitable results may be achieved ifthe described techniques are performed in a different order and/or ifcomponents in a described system, architecture, device, or circuit arecombined in a different manner and/or replaced or supplemented by othercomponents or their equivalents.

Accordingly, other implementations are within the scope of the followingclaims.

What is claimed is:
 1. A precoder for mitigating distortions of acommunication signal, the precoder implemented at a transmitter andcomprising: a filter configured to generate a filtering signal based ona third signal and filter coefficients corresponding to a selectedsignal generated based on a first signal, a second signal, and the thirdsignal, wherein the filter coefficients have nonlinear characteristicsand are selected such that the filter compensates for nonlineardistortions; and a modulo operator configured to generate the thirdsignal by performing a modulo operation on the second signal, whereinthe second signal is generated based on the first signal and thefiltering signal.
 2. The precoder of claim 1, wherein the filtercomprises: a level detector configured to generate the selected signal;a plurality of delay elements configured to output delayed signals bydelaying the third signal; a plurality of selectors configured to selectand output the filter coefficients based on the selected signal; aplurality of multipliers configured to multiply the third signal and thedelayed signals by the filter coefficients; and an adder configured tooutput the filtering signal by adding multiplication results obtained bythe plurality of multipliers.
 3. The precoder of claim 2, wherein thelevel detector comprises: an adder configured to generate a level signalbased on the first to third signals; and a comparator configured tooutput the selected signal based on the level signal and a plurality ofcomparison signals.
 4. The precoder of claim 2, wherein the plurality ofdelay elements comprises: a first delay element configured to output afirst delayed signal by delaying the third signal; and a second delayelement configured to output a second delayed signal by delaying thefirst delayed signal.
 5. The precoder of claim 4, wherein the pluralityof selectors comprises: a first selector configured to output a firstfilter coefficient corresponding to, the third signal; a second selectorconfigured to output a second filter coefficient corresponding to thefirst delayed signal; and a third selector configured to output a thirdfilter coefficient corresponding to the second delayed signal.
 6. Aprecoder for mitigating distortions of a communication signal, theprecoder implemented at a transmitter and comprising: a filterconfigured to generate a filtering signal based on a third signal andfilter coefficients respectively corresponding to a plurality ofselected signals generated based on a first signal, a second signal, andthe third signal, wherein the filter coefficients have nonlinearcharacteristics and are selected such that the filter compensates fornonlinear distortions; and a modulo operator configured to generate thethird signal by performing a modulo operation on the second signal,wherein the second signal is generated based on the first signal and thefiltering signal.
 7. The precoder of claim 6, wherein the filtercomprises: a level detector configured to generate the plurality ofselected signals; a plurality of delay elements configured to outputdelayed signals by delaying the third signal; a plurality of selectorsconfigured to select and output the filter coefficients based on theplurality of selected signals respectively; a plurality of multipliersconfigured to multiply the third signal and the delayed signals by thefilter coefficients; and an adder configured to output the filteringsignal by adding multiplication results obtained by the plurality ofmultipliers.
 8. The precoder of claim 7, wherein the level detectorcomprises: an adder configured to generate a level signal based on thefirst to third signals; a plurality of delay elements configured tooutput delayed signals by delaying the level signal; and a plurality ofcomparators configured to output the plurality of selected signals basedon the level signal and the delayed level signals respectively.
 9. Amethod for precoding to mitigate distortions of a communication signal,the method performed at a transmitter and comprising: generating afiltering based on a third signal and filter coefficients selected basedon a selected signal generated based on a first signal, a second signal,and the third signal, wherein the filter coefficients have nonlinearcharacteristics and are selected so as to compensate for nonlineardistortions; and generating the third signal by performing a modulooperation on the second signal, wherein the second signal is generatedbased on the first signal and the filtering signal.
 10. The method ofclaim 9, wherein the generating of the filtering signal comprises:generating the selected signal; outputting delayed signals by delayingthe third signal; selecting and, outputting the filter coefficientsbased on the selected signal; multiplying the third signal and thedelayed signals by the filter coefficients; and outputting the filteringsignal by adding multiplication results.
 11. The method of claim 10,wherein the generating of the selected signal comprises: generating alevel signal based on the first to third signals; and outputting theselected signal based on the level signal and a plurality of comparisonsignals.
 12. The method of claim 10, wherein the outputting by delayingcomprises: outputting a first delayed signal by delaying the thirdsignal; and outputting a second delayed signal by delaying the firstdelayed signal.
 13. The method of claim 12, wherein the selecting andoutputting of the filter coefficients comprises: outputting a firstfilter coefficient corresponding to the third signal; outputting asecond filter coefficient corresponding to the first delayed signal; andoutputting a third filter coefficient corresponding to the seconddelayed signal.
 14. The method of claim 9, wherein the outputting of thefiltering signal comprises: generating a plurality of selected signals;outputting the delayed signals by delaying the third signal; selectingand outputting the filter coefficients based on the plurality ofselected signals respectively; multiplying the third signal and thedelayed signal by the filter coefficients; and outputting the filteringsignal by adding multiplication results.
 15. The method of claim 14,wherein the generating of the plurality of selected signals comprises:generating a level signal based on the first to third signals;outputting delayed level signals by delaying the level signal; andoutputting the plurality of selected signals based on the level signaland the delayed level signals respectively.